Confidence Intervals that Utilize Uncertain Prior Information about Exogeneity in Panel Data

TL;DR

This paper develops a new confidence interval for a slope parameter in panel data models that effectively incorporates uncertain prior information about exogeneity, maintaining coverage probability while reducing expected length when prior assumptions hold.

Contribution

It introduces a novel confidence interval that leverages uncertain prior exogeneity information, balancing coverage probability and interval length adaptively.

Findings

Interval has near-nominal coverage probability.

Expected length is substantially reduced when prior is correct.

Interval adapts well when data contradict prior information.

Abstract

Consider panel data modelled by a linear random intercept model that includes a time-varying covariate. Suppose that we have uncertain prior information that this covariate is exogenous. We present a new confidence interval for the slope parameter that utilizes this uncertain prior information. This interval has minimum coverage probability very close to its nominal coverage. Let the scaled expected length of this new confidence interval be its expected length divided by the expected length of the confidence interval, with the same minimum coverage, constructed using the fixed effects model. This new interval has scaled expected length that (a) is substantially less than 1 when the prior information is correct, (b) has a maximum value that is not too much larger than 1 and (c) is close to 1 when the data strongly contradict the prior information. We illustrate the properties of this new interval using an airfare data set.